# Tagged Questions

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### Partition function proof

I am looking for any online information regarding Hardy and Ramanujan's proof, perhaps the proof itself, that the partition function $p(n)$ is asymptotic to $$\frac{e^{K\sqrt{n}}}{4n\sqrt{3}}$$ where ...
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### Best self study book with answers to selected questions for analytic number theory?

All: Can anyone recommend Best self study book with answers to selected questions for analytic number theory ? If a book have no answers to questions, but if you know if some professors choose the ...
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### which algebraic number theory book with answers to selected questions for self-study?

All: Can anyone recommend some easy to follow algebraic number theory books with answers (hints) to selected questions for self-study ? If a have no answers to questions, but if you know if some ...
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### Is there any book/resource which explain the general idea of the proof of Fermat's last theorem?

I look for a book/resource which display the general idea of the proof of Fermat last theorem in a simple manner for the public. I mean, books which is not for mathematicians but for the general ...
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### Ehrhart Polynomials Modulo Prime Integers

Are there any results known about computing Ehrhart Polynomials modulo prime integers?
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### Periodicity with irrational numbers

Recently, I invented the following theorem and found a proof, it seems strange since it is very counter-intuitive to me. The proof is long and non-conceptual. Is there a place or a branch of math ...
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### Who should I ask for Robin's paper? At any rate, I want to find out if a similar result to his can be achieved with 36 instead of 12.

Robin proved unconditionally that for $\ n \ge 3$ , $$\sigma(n)<\left(e^\gamma+{\log\log12\left({\frac73}-e^\gamma \log\log12\right)\over (\log \log n)^2}\right)n \log \log n.$$ I need a similar ...
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### Any Computational Number Theory Book, include software programs for key steps of the proofs of major theorem?

All: Can anyone recommend some Computational Number Theory Books, which include software programs for key steps of the proofs of major theorem ? Some computational number theory books only include ...
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### What is the latest that we know about odd perfect numbers?

What is the latest that we know about odd perfect numbers? I have seen some recent papers by Nielsen, and Ochem & Rao. I was wondering if there are any others.
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### The smallest class of numbers closed under addition, multiplication, and exponentiation

Let $\def\A{\mathfrak A}\A$ be the smallest subset of $\Bbb C$ that contains the algebraic numbers and also all numbers of the form $$\sum \alpha_i^{\beta_i}$$ where the $\alpha_i, \beta_i$ are ...
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### Recommendation for Number Theory Textbook

. Greetings, every mathematicians! I'm a foreigner (meaning English is not my first language) and an undergraduate student. I'm currently studying linear algebra, set theory and have already studied ...
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### $\lim _{x \to \infty} \sum_{p\leq x, p \equiv 1(mod k)} \frac {log(p)}{p}= \infty$

Where can I find a proof of the following equation? $\lim _{x \to \infty}\sum_{p\leq x,p \equiv 1(mod k)} \frac {log(p)}{p}= \infty$ where p is prime. The proof should be as elementary as ...
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### Gowers' proof of Szemerdi's theorem

Are there any good books or other resources (expository notes) which explains Gowers' proof of Szemerdi's theorem in detail?
I've been told that the asymptotic formula $\pi(x+y)-\pi(x)\sim y/\ln x$ holds for $y\ge x^{1/2+\varepsilon}$ if Riemann's hypothesis is true, but I was unable to find a journal reference for this. ...
I am looking at Dudley's proof of the existence of Mill's constant. It starts out as follows The proof depends on the following theorem: there is an integer $A$ such that if $n>A$, then there ...